The club – which was knocked out of the competition by Sunderland last season – has been beaten in both group games this campaign, suffering defeats to Shrewsbury Town and Macclesfield Town.
With no chance of qualifying for the next round, the Academy side will be aiming to restore pride against League Two Port Vale.
Lewis Cass is hoping United can impress on their last outing in the competition this season.
“It'll be a tough game,” said the 19-year-old defender. “We're expecting them to be very physical, but if we can get the ball down and play our football, then we'll hopefully be able to pass them off the park.
“We're going there hoping to try and progress from the game. We want to use this game as a stepping stone for when we play in the league.
“Our main objective is to try and finish as high as we can in the league – and as far as we can in cup competitions. Although, we can't progress in this, we want to use it as momentum to keep going.”
Vale have won both of their games so far in the competition, and are coming into the game on the back of an impressive 1-0 victory over League One side MK Dons in the FA Cup on Saturday.
Cass is expecting a tough game, but hopes that the young Newcastle squad can learn from the experience of playing EFL opposition.
“It's a young side at the minute, because of a few injuries,” Cass told the club’s official website.
“The lads who are in the physio room are working hard to get back on to the pitch, and those who have came into the team are doing very well. They're younger lads, but it's all about getting experience and playing against men will be another big step for them.”
The two sides have history in this competition, with Vale running out 1-0 winners in October 2017.
Meanwhile, Under-23 coach Neil Redfearn stepped down from his post at the club last week.